Question

A non vector `veca` is parallel to the line of intersection of the plane determined by the vectors `hati,hati+hatj` and thepane determined by the vectors `hati-hatj,hati+hatk` then angle between `veca and hati-2hatj+2hatk` is = (A) `pi/2` (B) `pi/3` (C) `pi/6` (D) `pi/4`
A. `(pi)/2`
B. `(pi)/3`
C. `(pi)/6`
D. `(pi)/4`

Answer 1

Correct Answer - D
The line of intersection of the two planes is perpendicular to their normals. So, it parallel to the vector
`veca={(hatixx(hati+hatj)}xx{(hati-hatj)xx(hati=hatk)}`
`impliesveca=hatkxx(-hatj+hatk-hatk)=hati-hatj`
Let `theta` be the angle between `veca` and `vecb-hati-2hatj+2hatk`. Then
`cos theta=(veca.vecb)/(|veca||vecb|)=3/(sqrt(2)xx3)=1/(sqrt(2))impliestheta=(pi)/4`